Golf ball

ABSTRACT

A golf ball  2  has a large number of dimples  8  on a surface thereof. A trajectory of the golf ball  2  is divided into first to fourth segments. An average CD1 of drag coefficients CD and an average CL1 of lift coefficients CL in the first segment are equal to or less than 0.225 and 0.180, respectively. An average CD2 of drag coefficients CD and an average CL2 of lift coefficients CL in the second segment are equal to or less than 0.250 and 0.220, respectively. An average CD3 of drag coefficients CD and an average CL3 of lift coefficients CL in the third segment are equal to or greater than 0.260 and 0.220, respectively. An average CD4 of drag coefficients CD and an average CL4 of lift coefficients CL in the fourth segment are equal to or greater than 0.250 and 0.200, respectively.

CROSS REFERENCE

The present application is a 37 C.F.R. §1.53(b) Continuation of, U.S.application Ser. No. 14/100,804, filed Dec. 9, 2013, which claimspriority under 35 U.S.C. §119(a) to Japanese Application No. 2012-286541filed on Dec. 28, 2012, all of which is hereby expressly incorporated byreference into the present application.

BACKGROUND OF THE INVENTION

Field of the Invention

The present invention relates to golf balls. Specifically, the presentinvention relates to improvement of dimples of golf balls.

Description of the Related Art

Golf balls have a large number of dimples on the surface thereof. Thedimples disturb the air flow around the golf ball during flight to causeturbulent flow separation. By causing the turbulent flow separation,separation points of the air from the golf ball shift backwards. Theturbulent flow separation promotes the displacement between theseparation point on the upper side and the separation point on the lowerside of the golf ball which results from the backspin.

A drag coefficient CD and a lift coefficient CL influence a trajectoryof a golf ball. The United States Golf Association (USGA) has released amanual for a trajectory calculation program. By inputting a dragcoefficient CD and a lift coefficient CL to a program that complies withthe manual, a flight distance of a golf ball can be predicted. The dragcoefficient CD and the lift coefficient CL are measured through the ITR(Indoor Test Range) specified in the rule of the USGA.

US2007/0093319 discloses a golf ball in which a lift force falls withina predetermined range at a Reynolds Number of 205000 and a spin rate of2900 rpm.

US2007/0093320 discloses a golf ball in which a drag coefficient CD anda lift coefficient CL fall within predetermined ranges at a ReynoldsNumber of 230000 and a spin ratio of 0.085.

The drag coefficient CD and the lift coefficient CL change moment bymoment from a launch point to a landing point. In the golf balldisclosed in US2007/0093319, the lift force at one time point in atrajectory is merely set within the predetermined range. Evaluationregarding the flight performance of the golf ball is not sufficient. Inthe golf ball disclosed in US2007/0093320, the drag coefficient CD andthe lift coefficient CL at one time point in a trajectory are merely setwithin the predetermined ranges. Evaluation regarding the flightperformance of the golf ball is also not sufficient.

An object of the present invention is to provide a golf ball havingexcellent flight performance.

SUMMARY OF THE INVENTION

A golf ball according to the present invention has a large number ofdimples on a surface thereof. In the golf ball, when a trajectory thatis calculated under conditions of a ball initial speed of 57.4 m/s, alaunch angle of 13.3°, and an initial backspin rate of 2450 rpm by aprogram created according to a manual provided by the USGA using a dragcoefficient CD and a lift coefficient CL obtained through an ITR, isdivided into a first segment, a second segment, a third segment, and afourth segment, an average of drag coefficients CD and an average oflift coefficients CL in each segment are as follows.

Average CD1 of drag coefficients CD in the first segment: equal to orless than 0.225

Average CL1 of lift coefficients CL in the first segment: equal to orless than 0.180

Average CD2 of drag coefficients CD in the second segment: equal to orless than 0.250

Average CL2 of lift coefficients CL in the second segment: equal to orless than 0.220

Average CD3 of drag coefficients CD in the third segment: equal to orgreater than 0.260

Average CL3 of lift coefficients CL in the third segment: equal to orgreater than 0.220

Average CD4 of drag coefficients CD in the fourth segment: equal to orgreater than 0.250

Average CL4 of lift coefficients CL in the fourth segment: equal to orgreater than 0.200

The first segment is a segment from a launch point to a midpoint betweenthe launch point and a top. The second segment is a segment from themidpoint between the launch point and the top to the top. The thirdsegment is a segment from the top to a midpoint between the top and alanding point. The fourth segment is a segment from the midpoint betweenthe top and the landing point to the landing point.

In the golf ball according to the present invention, the dragcoefficients CD and the lift coefficients CL from the launch point tothe landing point are appropriate. The golf ball has excellent flightperformance.

Preferably, a contour shape of each dimple is non-circular. Preferably,each dimple is obtained based on a contour of a Voronoi region assumedon a surface of a phantom sphere of the golf ball.

Preferably, a pattern of the dimples is obtained by a designing processcomprising the steps of:

(1) assuming a large number of circles on the surface of the phantomsphere;

(2) assuming a large number of generating points based on positions ofthe large number of circles;

(3) assuming a large number of Voronoi regions on the surface of thephantom sphere by a Voronoi tessellation based on the large number ofgenerating points; and

(4) assigning a dimple and a land to the surface of the phantom spherebased on contours of the large number of Voronoi regions.

Preferably, a radius variation range Rh of each dimple is equal to orgreater than 0.4 mm. Preferably, each dimple meets the followingmathematical formula.Rh/Rave≧0.25In the mathematical formula, Rh represents a radius variation range, andRave represents an average radius.

Preferably, a difference between a radius variation range Rhmax of adimple having a maximum radius variation range Rh and a radius variationrange Rhmin of a dimple having a minimum radius variation range Rh isequal to or greater than 0.1 mm.

Preferably, the golf ball meets the following mathematical formula.(Rhmax−Rhmin)>(R1−R2)In the mathematical formula, Rhmax represents a radius variation rangeof a dimple having a maximum radius variation range Rh, Rhmin representsa radius variation range of a dimple having a minimum radius variationrange Rh, R1 represents an average radius of the dimple having a maximumradius variation range Rh, and R2 represents an average radius of thedimple having a minimum radius variation range Rh.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic cross-sectional view of a golf ball according toone embodiment of the present invention;

FIG. 2 is an enlarged front view of the golf ball in FIG. 1;

FIG. 3 is a plan view of the golf ball in FIG. 2;

FIG. 4 is a front view of a phantom sphere in which a large number ofcircles are assumed on a surface thereof;

FIG. 5 is a plan view of the phantom sphere in FIG. 4;

FIG. 6 is a front view of a phantom sphere in which a large number ofgenerating points are assumed on a surface thereof;

FIG. 7 is a plan view of the phantom sphere in FIG. 6;

FIG. 8 is an enlarged view showing the generating points in FIG. 6 withVoronoi regions;

FIG. 9 is a front view of a mesh used in a Voronoi tessellation;

FIG. 10 is a front view of a phantom sphere in which Voronoi regionsobtained by a simple method are assumed;

FIG. 11 is a plan view of the phantom sphere in FIG. 10;

FIG. 12 is an enlarged view of a dimple of the golf ball in FIG. 2;

FIG. 13 is a graph for explaining a method for calculating a radiusvariation range of the dimple in FIG. 12;

FIG. 14 is a graph showing a trajectory of the golf ball in FIG. 2 witha drag coefficient CD and a lift coefficient CL;

FIG. 15 is a front view of a golf ball having a pattern A;

FIG. 16 is a plan view of the golf ball in FIG. 15;

FIG. 17 is a front view of a golf ball having a pattern B;

FIG. 18 is a plan view of the golf ball in FIG. 17;

FIG. 19 is a graph showing an aerodynamic map in a first segment;

FIG. 20 is a graph showing another aerodynamic map in the first segment;

FIG. 21 is a graph showing an aerodynamic map in a second segment;

FIG. 22 is a graph showing another aerodynamic map in the secondsegment;

FIG. 23 is a graph showing an aerodynamic map in a third segment;

FIG. 24 is a graph showing another aerodynamic map in the third segment;

FIG. 25 is a graph showing an aerodynamic map in a fourth segment; and

FIG. 26 is a graph showing another aerodynamic map in the fourthsegment.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The following will describe in detail the present invention based onpreferred embodiments with reference to the accompanying drawings.

A golf ball 2 shown in FIG. 1 includes a spherical core 4 and a cover 6.On the surface of the cover 6, a large number of dimples 8 are formed.Of the surface of the golf ball 2, a part other than the dimples 8 is aland 10. The golf ball 2 includes a paint layer and a mark layer on theexternal side of the cover 6 although these layers are not shown in thedrawing. A mid layer may be provided between the core 4 and the cover 6.

The golf ball 2 has a diameter of preferably 40 mm or greater but 45 mmor less. From the standpoint of conformity to the rules established bythe United States Golf Association (USGA), the diameter is particularlypreferably equal to or greater than 42.67 mm. In light of suppression ofair resistance, the diameter is more preferably equal to or less than 44mm and particularly preferably equal to or less than 42.80 mm. The golfball 2 has a weight of preferably 40 g or greater but 50 g or less. Inlight of attainment of great inertia, the weight is more preferablyequal to or greater than 44 g and particularly preferably equal to orgreater than 45.00 g. From the standpoint of conformity to the rulesestablished by the USGA, the weight is particularly preferably equal toor less than 45.93 g.

The core 4 is formed by crosslinking a rubber composition. Examples ofbase rubbers for use in the rubber composition include polybutadienes,polyisoprenes, styrene-butadiene copolymers, ethylene-propylene-dienecopolymers, and natural rubbers. Two or more rubbers may be used incombination. In light of resilience performance, polybutadienes arepreferred, and, high-cis polybutadienes are particularly preferred.

In order to crosslink the core 4, a co-crosslinking agent can be used.Examples of preferable co-crosslinking agents in light of resilienceperformance include zinc acrylate, magnesium acrylate, zincmethacrylate, and magnesium methacrylate. Preferably, the rubbercomposition includes an organic peroxide together with a co-crosslinkingagent. Examples of suitable organic peroxides include dicumyl peroxide,1,1-bis(t-butylperoxy)-3,3,5-trimethylcyclohexane,2,5-dimethyl-2,5-di(t-butylperoxy)hexane, and di-t-butyl peroxide.

According to need, various additives such as sulfur, a sulfur compound,a filler, an anti-aging agent, a coloring agent, a plasticizer, adispersant, and the like are included in the rubber composition of thecore 4 in an adequate amount. Crosslinked rubber powder or syntheticresin powder may also be included in the rubber composition.

The core 4 has a diameter of preferably 30.0 mm or greater andparticularly preferably 38.0 mm or greater. The diameter of the core 4is preferably equal to or less than 42.0 mm and particularly preferablyequal to or less than 41.5 mm. The core 4 may be composed of two or morelayers. The core 4 may have a rib on its surface. The core 4 may behollow.

A suitable polymer for the cover 6 is an ionomer resin. Examples ofpreferable ionomer resins include binary copolymers formed with anα-olefin and an α,β-unsaturated carboxylic acid having 3 to 8 carbonatoms. Examples of other preferable ionomer resins include ternarycopolymers formed with: an α-olefin; an α,β-unsaturated carboxylic acidhaving 3 to 8 carbon atoms; and an α,β-unsaturated carboxylate esterhaving 2 to 22 carbon atoms. For the binary copolymers and ternarycopolymers, preferable α-olefins are ethylene and propylene, whilepreferable α,β-unsaturated carboxylic acids are acrylic acid andmethacrylic acid. In the binary copolymers and ternary copolymers, someof the carboxyl groups are neutralized with metal ions. Examples ofmetal ions for use in neutralization include sodium ion, potassium ion,lithium ion, zinc ion, calcium ion, magnesium ion, aluminum ion, andneodymium ion.

Another polymer may be used instead of or together with an ionomerresin. Examples of the other polymer include thermoplastic polyurethaneelastomers, thermoplastic styrene elastomers, thermoplastic polyamideelastomers, thermoplastic polyester elastomers, and thermoplasticpolyolefin elastomers. In light of spin performance, thermoplasticpolyurethane elastomers are preferred.

According to need, a coloring agent such as titanium dioxide, a fillersuch as barium sulfate, a dispersant, an antioxidant, an ultravioletabsorber, a light stabilizer, a fluorescent material, a fluorescentbrightener, and the like are included in the cover 6 in an adequateamount. For the purpose of adjusting specific gravity, powder of a metalwith a high specific gravity such as tungsten, molybdenum, and the likemay be included in the cover 6.

The cover 6 has a thickness of preferably 0.1 mm or greater andparticularly preferably 0.3 mm or greater. The thickness of the cover 6is preferably equal to or less than 2.5 mm and particularly preferablyequal to or less than 2.2 mm. The cover 6 has a specific gravity ofpreferably 0.90 or greater and particularly preferably 0.95 or greater.The specific gravity of the cover 6 is preferably equal to or less than1.10 and particularly preferably equal to or less than 1.05. The cover 6may be composed of two or more layers.

FIG. 2 is an enlarged front view of the golf ball 2 in FIG. 1. FIG. 3 isa plan view of the golf ball 2 in FIG. 2. As is obvious from FIGS. 2 and3, the golf ball 2 has a large number of non-circular dimples 8. Bythese dimples 8 and the land 10, a rugged pattern is formed on thesurface of the golf ball 2.

In a process for designing the rugged pattern, a Voronoi tessellation isused. In the designing process, a large number of generating points arearranged on the surface of a phantom sphere 12 (see FIG. 1). A largenumber of regions are assumed on the surface of the phantom sphere 12based on the generating points by the Voronoi tessellation. In thepresent specification, these regions are referred to as “Voronoiregions”. Dimples 8 and a land 10 are assigned based on the contours ofthese Voronoi regions. The designing process is preferably executedusing a computer and software in light of efficiency. Of course, thepresent invention is practicable even by hand calculation. The essenceof the present invention is not in a computer and software. Thefollowing will describe the designing process in detail.

In the designing process, as shown in FIGS. 4 and 5, a large number ofcircles 14 are assumed on the surface of the phantom sphere 12. Themethod for assuming these circles 14 is the same as a process fordesigning a dimple pattern having circular dimples. The process fordesigning a dimple pattern having circular dimples is well known to oneskilled in the art. Each of the circles 14 coincides with the contour ofa circular dimple. In the present embodiment, the number of the circles14 is 344.

A large number of generating points are assumed on the surface of thephantom sphere 12 based on the positions of these circles 14. In thepresent embodiment, the center of each circle 14 is assumed as agenerating point. FIGS. 6 and 7 show these generating points 16. In thepresent embodiment, since the number of the circles 14 is 344, thenumber of the generating points 16 is 344.

A large number of Voronoi regions are assumed based on these generatingpoints 16. FIG. 8 shows the Voronoi regions 18. In FIG. 8, a generatingpoint 16 a is adjacent to six generating points 16 b. What is indicatedby each reference sign 20 is a line segment connecting the generatingpoint 16 a to the generating point 16 b. FIG. 8 shows six line segments20. What is indicated by each reference sign 22 is the perpendicularbisector of each line segment 20. The generating point 16 a issurrounded by six perpendicular bisectors 22. What is indicated by eachoutline circle in FIG. 8 is the intersection point between aperpendicular bisector 22 and another perpendicular bisector 22. A pointobtained by projecting the intersection point onto the surface of thephantom sphere 12 is a vertex of a spherical polygon (e.g., a sphericalhexagon). This projection is performed by light emitted from the centerof the phantom sphere 12. The spherical polygon is a Voronoi region 18.The surface of the phantom sphere 12 is divided into a large number ofthe Voronoi regions 18. The method for the division is referred to as aVoronoi tessellation. In the present embodiment, since the number of thegenerating points 16 is 344, the number of the Voronoi regions 18 is344.

Calculation for defining the contour of each Voronoi region 18 based onthe perpendicular bisectors 22 is complicated. The following willdescribe a method for simply obtaining Voronoi regions 18. In themethod, the surface of the phantom sphere 12 is divided into a largenumber of spherical triangles. This division is performed based on anadvancing front method. The advancing front method is disclosed at Pages195 to 197 of “Daigakuin Johoshorikogaku 3, Keisan Rikigaku (InformationScience and Technology for Graduate School 3, Computational Dynamics)”(edited by Koichi ITO, published by Kodansha Ltd.). A mesh 24 shown inFIG. 9 is obtained by this division. The mesh 24 has 314086 trianglesand 157045 vertices. Each vertex is defined as a cell (or the center ofa cell). The mesh 24 has 157045 cells. The phantom sphere 12 may bedivided by other methods. The number of the cells is preferably equal toor greater than 10000 and particularly preferably equal to or greaterthan 100000.

The distances between each cell in the mesh 24 and all the generatingpoints 16 are calculated. For each cell, distances of which the numberis the same as the number of the generating points 16 are calculated.The shortest distance is selected from among these distances. The cellis associated with the generating point 16 on which the shortestdistance is based. In other words, the generating point 16 that isclosest to the cell is selected. It is noted that calculation of thedistances between the cell and the generating points 16 whose distancesfrom the cell are obviously large may be omitted.

For each generating point 16, a set of cells associated with thegenerating point 16 is assumed. In other words, a set of cells for whichthis generating point 16 is the closest generating point 16 is assumed.The set is set as a Voronoi region 18. A large number of the Voronoiregions 18 obtained thus are shown in FIGS. 10 and 11. In FIGS. 10 and11, when another cell adjacent to a certain cell belongs to a Voronoiregion 18 different from a Voronoi region 18 to which the certain cellbelongs, the certain cell is filled with black.

As is obvious from FIGS. 10 and 11, the contour of each Voronoi region18 is a zigzag contour. This contour is subjected to smoothing or thelike. Typical smoothing is moving averaging. Smoothing by three-pointmoving average, five-point moving average, seven-point moving average,or the like can be used.

In the three-point moving average, coordinates of the following threecells are averaged:

(1) a cell;

(2) a cell that is closest to the cell in a clockwise direction; and

(3) a cell that is closest to the cell in a counterclockwise direction.

In the five-point moving average, coordinates of the following fivecells are averaged:

(1) a cell;

(2) a cell that is closest to the cell in the clockwise direction;

(3) a cell that is closest to the cell in the counterclockwisedirection;

(4) a cell that is second closest to the cell in the clockwisedirection; and

(5) a cell that is second closest to the cell in the counterclockwisedirection.

In the seven-point moving average, coordinates of the following sevencells are averaged:

(1) a cell;

(2) a cell that is closest to the cell in the clockwise direction;

(3) a cell that is closest to the cell in the counterclockwisedirection;

(4) a cell that is second closest to the cell in the clockwisedirection;

(5) a cell that is second closest to the cell in the counterclockwisedirection;

(6) a cell that is third closest to the cell in the clockwise direction;and

(7) a cell that is third closest to the cell in the counterclockwisedirection.

A plurality of points having the coordinates obtained by the movingaverage are connected to each other by a spline curve. A loop isobtained by the spline curve. When forming a loop, some of the pointsmay be removed, and a spline curve may be drawn. The loop may beenlarged or reduced in size to obtain a new loop. A land 10 is assignedonto the loop or to the outside of the loop. In other words, a land 10is assigned to the vicinity of the contour of the Voronoi region 18.Meanwhile, a dimple 8 is assigned to the inside of the loop or onto theloop. In this manner, a rugged pattern shown in FIGS. 2 and 3 isobtained.

In light of flight performance of the golf ball 2, the occupation ratioof the dimples 8 is preferably equal to or greater than 85%, morepreferably equal to or greater than 90%, and particularly preferablyequal to or greater than 92%. In light of durability of the golf ball 2,the occupation ratio is preferably equal to or less than 98%. In thepresent embodiment, the occupation ratio is 92%. Use of the Voronoitessellation achieves a high occupation ratio even when no small dimple8 is arranged.

As is obvious from FIGS. 2 and 3, the dimples 8 are not orderly arrangedin the golf ball 2. The golf ball 2 has a large number of types ofdimples 8 whose contour shapes are different from each other. Thesedimples 8 achieve a superior dimple effect. The number of the types ofthe dimples 8 is preferably equal to or greater than 50 and particularlypreferably equal to or greater than 100. In the present embodiment, eachdimple has a contour shape different from those of any other dimples.

In light of suppression of rising of the golf ball 2 during flight, eachdimple 8 has a depth of preferably 0.05 mm or greater, more preferably0.08 mm or greater, and particularly preferably 0.10 mm or greater. Inlight of suppression of dropping of the golf ball 2 during flight, thedepth is preferably equal to or less than 0.60 mm, more preferably equalto or less than 0.45 mm, and particularly preferably equal to or lessthan 0.40 mm. The depth is the distance between the deepest point of thedimple 8 and the surface of the phantom sphere 12.

In the present invention, the term “dimple volume” means the volume of apart surrounded by the surface of the phantom sphere 12 and the surfaceof the dimple 8. In light of suppression of rising of the golf ball 2during flight, the sum of the volumes (total volume) of all the dimples8 is preferably equal to or greater than 500 mm³, more preferably equalto or greater than 550 mm³, and particularly preferably equal to orgreater than 600 mm³. In light of suppression of dropping of the golfball 2 during flight, the sum is preferably equal to or less than 900mm³, more preferably equal to or less than 850 mm³, and particularlypreferably equal to or less than 800 mm³.

From the standpoint that a fundamental feature of the golf ball 2 beingsubstantially a sphere is not impaired, the total number of the dimples8 is preferably equal to or greater than 250, more preferably equal toor greater than 280, and particularly preferably equal to or greaterthan 310. From the standpoint that each dimple 8 can contribute to thedimple effect, the total number is preferably equal to or less than 450,more preferably equal to or less than 400, and particularly preferablyequal to or less than 370.

As described above, prior to the Voronoi tessellation, a large number ofthe circles 14 are assumed on the surface of the phantom sphere 12. Fromthe standpoint that the dimples 8 can be uniformly arranged, it ispreferred that the circles 14 are assumed such that one or more ofconditions indicated in the following (1) to (4) are met.

(1) Each circle 14 does not intersect other circles 14 adjacent to thecircle 14.

(2) The diameter of each circle 14 is equal to or greater than 2.0 mmbut equal to or less than 6.0 mm.

(3) The number of the circles 14 is equal to or greater than 280 butequal to or less than 400.

(4) The ratio of the total area of the circles 14 to the area of thesurface of the phantom sphere 12 is equal to or greater than 60%.

Preferably, the circles 14 are assumed such that all the conditionsindicated in the above (1) to (4) are met.

The golf ball 2 has dimples 8 having a radius variation range Rh of 0.4mm or greater. A method for calculating a radius variation range Rh isshown in FIG. 12. In this method, 30 points P are assumed on the contourof the dimple 8 such that the length of the contour is divided into 30equal parts. These points P include a point Pp that is located on thecontour of the dimple 8 and closest to a pole. A coordinate of a centerO is decided by averaging coordinates of the 30 points P.

After the coordinate of the center O is decided, the distance betweenthe center O and the point P (i.e., a radius R) is calculated. For eachpoint P, the radius R is calculated. FIG. 13 is a graph in which theradius R is plotted. The horizontal axis of the graph indicates an angleof a line connecting the center O to each point, relative to a longitudedirection. As shown in the graph, a value obtained by subtracting theminimum value of the radius R from the maximum value of the radius R isthe radius variation range Rh. The radius variation range Rh is an indexindicating distortion of the dimple 8.

In the golf ball 2 having the dimples 8 having a radius variation rangeRh of 0.4 mm or greater, the dimples 8 are not orderly arranged. Thegolf ball 2 has excellent flight performance. The ratio P1 of the numberof the dimples 8 having a radius variation range Rh of 0.4 mm or greaterrelative to the total number of the dimples 8 is preferably equal to orgreater than 30%, more preferably equal to or greater than 50%, andparticularly preferably equal to or greater than 70%. The ratio P1 isideally 100%. In the golf ball 2 shown in FIGS. 2 and 3, the ratio P1 is81%.

As is obvious from FIG. 13, variation of the radius R of the dimple 8 isnot periodic. In the golf ball 2, the dimples 8 are not orderlyarranged. The golf ball 2 has excellent flight performance.

In light of flight performance, the difference between the radiusvariation range Rhmax of the dimple 8 having a maximum radius variationrange Rh and the radius variation range Rhmin of the dimple 8 having aminimum radius variation range Rh is preferably equal to or greater than0.1 mm, more preferably equal to or greater than 0.3 mm, andparticularly preferably equal to or greater than 0.5 mm.

In light of flight performance, the standard deviation of the radiusvariation ranges Rh of all the dimples 8 is preferably equal to orgreater than 0.10 and particularly preferably equal to or greater than0.13.

The golf ball 2 has dimples 8 that meet the following mathematicalformula (1).Rh/Rave≧0.25  (1)In this mathematical formula, Rh represents a radius variation range,and Rave represents an average radius. Rave is the average of the radiiR at all points that a single dimple 8 has.

In the golf ball 2 that meet the above mathematical formula (1), thedimples 8 are not orderly arranged. The golf ball 2 has excellent flightperformance. The ratio P2 of the number of the dimples 8 that meet theabove mathematical formula (1), relative to the total number of thedimples 8, is preferably equal to or greater than 10%, more preferablyequal to or greater than 20%, and particularly preferably equal to orgreater than 30%. The ratio P2 is ideally 100%. In the golf ball 2 shownin FIGS. 2 and 3, the ratio P2 is 36%.

In light of flight performance, it is preferred that the golf ball 2meets the following mathematical formula (2).(Rhmax−Rhmin)>(R1−R2)  (2)In the mathematical formula, Rhmax represents the radius variation rangeof the dimple 8 having a maximum radius variation range Rh, Rhminrepresents the radius variation range of the dimple 8 having a minimumradius variation range Rh, R1 represents the average radius of thedimple 8 having a maximum radius variation range Rh, and R2 representsthe average radius of the dimple 8 having a minimum radius variationrange Rh. The difference between (Rhmax−Rhmin) and (R1−R2) is preferablyequal to or greater than 0.1 mm, more preferably equal to or greaterthan 0.2 mm, and particularly preferably equal to or greater than 0.3mm. In the golf ball 2 shown in FIGS. 2 and 3, the difference is 0.449mm.

A drag coefficient CD and a lift coefficient CL of the golf ball 2 under15 conditions are measured through the ITR. A trajectory of the golfball 2 is calculated by a program created according to the manualprovided by the USGA, using the drag coefficient CD and the liftcoefficient CL. The following conditions are also inputted to theprogram.

Ball initial speed of: 57.4 m/s

Launch angle: 13.3°

Initial backspin rate: 2450 rpm

In this program, a trajectory is calculated based on a model which isproposed by “S. J. Quintavalla” of the USGA. This model is disclosed in“Science and Golf IV, Chapter 30, A Generally Applicable Model for theAerodynamic Behavior of Golf Balls” published in 2002.

The drag coefficient CD and the lift coefficient CL can be calculatedevery 5/1000 sec from a launch point to a landing point by thetrajectory calculation. A locus, the drag coefficient CD, and the liftcoefficient CL which are obtained by the trajectory calculation areshown in FIG. 14. The locus of the trajectory of the golf ball 2gradually rises from the launch point to the top and gradually fallsfrom the top to the landing point.

In FIG. 14, segments of the trajectory are indicated by reference signsI to IV. What is indicated by the reference sign I is a first segment,what is indicated by the reference sign II is a second segment, what isindicated by the reference sign III is a third segment, and what isindicated by the reference sign IV is a fourth segment. The boundarybetween the first segment and the second segment is the midpoint betweenthe launch point and the top. The boundary between the second segmentand the third segment is the top. The boundary between the third segmentand the fourth segment is the midpoint between the top and the landingpoint. The horizontal distance of the first segment is the same as thatof the second segment. The horizontal distance of the third segment isthe same as that of the fourth segment.

In the present invention, each of a large number of drag coefficients CDis calculated every 5/1000 sec. In addition, the average of the dragcoefficients CD that belong to each segment is calculated. Specifically,the average CD1 of the drag coefficients CD in the first segment, theaverage CD2 of the drag coefficients CD in the second segment, theaverage CD3 of the drag coefficients CD in the third segment, and theaverage CD4 of the drag coefficients CD in the fourth segment arecalculated.

In the present invention, each of a large number of lift coefficients CLis calculated every 5/1000 sec. In addition, the average of the liftcoefficients CL that belong to each segment is calculated. Specifically,the average CL1 of the lift coefficients CL in the first segment, theaverage CL2 of the lift coefficients CL in the second segment, theaverage CL3 of the lift coefficients CL in the third segment, and theaverage CL4 of the lift coefficients CL in the fourth segment arecalculated.

The specifications of golf balls according to Samples 1 to 10 for whichaverages of the drag coefficients CD and the averages of the liftcoefficients CL are calculated are shown in Table 1 below.

TABLE 1 Specifications of Golf Balls Total Front Plan volume Patternview view (mm³) Sample 1 A FIG. 15 FIG. 16 532 Sample 2 A FIG. 15 FIG.16 552 Sample 3 A FIG. 15 FIG. 16 572 Sample 4 B FIG. 17 FIG. 18 536Sample 5 B FIG. 17 FIG. 18 556 Sample 6 B FIG. 17 FIG. 18 576 Sample 7 CFIG. 2 FIG. 3 670 Sample 8 C FIG. 2 FIG. 3 690 Sample 9 C FIG. 2 FIG. 3710 Sample 10 C FIG. 2 FIG. 3 730

Trajectory calculation is performed with changing the average CD1 andthe average CL1 in the first segment of the golf ball according toSample 2 in the above Table 1, and flight distances are calculated.Contour lines for the flight distances are shown in an aerodynamic mapin FIG. 19. The gradients of the contour lines are identified from theaerodynamic map. The gradients of the contour lines are substantiallythe same as those in the first segment of another golf ball when a ballinitial speed, a launch angle, and an initial backspin rate are the sametherebetween. Therefore, the gradients can be universally used asgradients of a general golf ball. FIG. 20 shows another aerodynamic map.In FIG. 20, the horizontal axis indicates the average CD1 in the firstsegment, and the vertical axis indicates the average CL1 in the firstsegment. In FIG. 20, the averages CD1 and the averages CL1 of the golfballs according to Samples 1 to 10 are plotted. What is indicated by analternate long and short dash line in FIG. 20 is the contour line forthe flight distance. A golf ball that is located on the left side of thecontour line and whose distance to the contour line is large hasexcellent flight performance.

Trajectory calculation is performed with changing the average CD2 andthe average CL2 in the second segment of the golf ball according toSample 2 in the above Table 1, and flight distances are calculated.Contour lines for the flight distances are shown in an aerodynamic mapin FIG. 21. The gradients of the contour lines are identified from theaerodynamic map. The gradients of the contour lines are substantiallythe same as those in the second segment of another golf ball when a ballinitial speed, a launch angle, and an initial backspin rate are the sametherebetween. Therefore, the gradients can be universally used asgradients of a general golf ball. FIG. 22 shows another aerodynamic map.In FIG. 22, the horizontal axis indicates the average CD2 in the secondsegment, and the vertical axis indicates the average CL2 in the secondsegment. In FIG. 22, the averages CD2 and the averages CL2 of the golfballs according to Samples 1 to 10 are plotted. What is indicated by analternate long and short dash line in FIG. 22 is the contour line forthe flight distance. A golf ball that is located on the left side of thecontour line and whose distance to the contour line is large hasexcellent flight performance.

Trajectory calculation is performed with changing the average CD3 andthe average CL3 in the third segment of the golf ball according toSample 2 in the above Table 1, and flight distances are calculated.Contour lines for the flight distances are shown in an aerodynamic mapin FIG. 23. The gradients of the contour lines are identified from theaerodynamic map. The gradients of the contour lines are substantiallythe same as those in the third segment of another golf ball when a ballinitial speed, a launch angle, and an initial backspin rate are the sametherebetween. Therefore, the gradients can be universally used asgradients of a general golf ball. FIG. 24 shows another aerodynamic map.In FIG. 24, the horizontal axis indicates the average CD3 in the thirdsegment, and the vertical axis indicates the average CL3 in the thirdsegment. In FIG. 24, the averages CD3 and the averages CL3 of the golfballs according to Samples 1 to 10 are plotted. What is indicated by analternate long and short dash line in FIG. 24 is the contour line forthe flight distance. A golf ball that is located on the left side of thecontour line and whose distance to the contour line is large hasexcellent flight performance.

Trajectory calculation is performed with changing the average CD4 andthe average CL4 in the fourth segment of the golf ball according toSample 2 in the above Table 1, and flight distances are calculated. Acontour line for the flight distance is shown in an aerodynamic map inFIG. 25. The gradient of the contour line is identified from theaerodynamic map. The gradient of the contour line is substantially thesame as that in the fourth segment of another golf ball when a ballinitial speed, a launch angle, and an initial backspin rate are the sametherebetween. Therefore, the gradient can be universally used as agradient of a general golf ball. FIG. 26 shows another aerodynamic map.In FIG. 26, the horizontal axis indicates the average CD4 in the fourthsegment, and the vertical axis indicates the average CL4 in the fourthsegment. In FIG. 26, the averages CD4 and the averages CL4 of the golfballs according to Samples 1 to 10 are plotted. What is indicated by analternate long and short dash line in FIG. 26 is a contour line for theflight distance. A golf ball that is located on the left side of thecontour line and whose distance to the contour line is large hasexcellent flight performance.

From FIGS. 20 and 22, it is recognized that a golf ball of which thedrag coefficients CD and the lift coefficients CL in the first segmentand the second segment are low has excellent flight performance. FromFIGS. 24 and 26, it is recognized that a golf ball of which the dragcoefficients CD and the lift coefficients CL in the third segment andthe fourth segment are high has excellent flight performance.

In light of flight performance, the average CD1 of the drag coefficientsCD in the first segment is preferably equal to or less than 0.225, morepreferably equal to or less than 0.224, and particularly preferablyequal to or less than 0.223. In light of flight performance, the averageCL1 of the lift coefficients CL in the first segment is preferably equalto or less than 0.180, more preferably equal to or less than 0.177, andparticularly preferably equal to or less than 0.175.

In light of flight performance, the average CD2 of the drag coefficientsCD in the second segment is preferably equal to or less than 0.250, morepreferably equal to or less than 0.245, and particularly preferablyequal to or less than 0.244. In light of flight performance, the averageCL2 of the lift coefficients CL in the second segment is preferablyequal to or less than 0.220, more preferably equal to or less than0.215, and particularly preferably equal to or less than 0.212.

In light of flight performance, the average CD3 of the drag coefficientsCD in the third segment is preferably equal to or greater than 0.260,more preferably equal to or greater than 0.265, and particularlypreferably equal to or greater than 0.270. In light of flightperformance, the average CL3 of the lift coefficients CL in the thirdsegment is preferably equal to or greater than 0.220, more preferablyequal to or greater than 0.230, and particularly preferably equal to orgreater than 0.239.

In light of flight performance, the average CD4 of the drag coefficientsCD in the fourth segment is preferably equal to or greater than 0.250,more preferably equal to or greater than 0.256, and particularlypreferably equal to or greater than 0.266. In light of flightperformance, the average CL4 of the lift coefficients CL in the fourthsegment is preferably equal to or greater than 0.200, more preferablyequal to or greater than 0.213, and particularly preferably equal to orgreater than 0.234.

EXAMPLES Example 1

A rubber composition was obtained by kneading 100 parts by weight of apolybutadiene (trade name “BR-730”, manufactured by JSR Corporation), 30parts by weight of zinc diacrylate, 6 parts by weight of zinc oxide, 10parts by weight of barium sulfate, 0.5 parts by weight of diphenyldisulfide, and 0.5 parts by weight of dicumyl peroxide. This rubbercomposition was placed into a mold including upper and lower mold halveseach having a hemispherical cavity, and heated at 170° C. for 18 minutesto obtain a core with a diameter of 39.7 mm. Meanwhile, a resincomposition was obtained by kneading 50 parts by weight of an ionomerresin (trade name “Himilan 1605”, manufactured by Du Pont-MITSUIPOLYCHEMICALS Co., LTD.), 50 parts by weight of another ionomer resin(trade name “Himilan 1706”, manufactured by Du Pont-MITSUI POLYCHEMICALSCo., LTD.), and 3 parts by weight of titanium dioxide. The above corewas placed into a final mold having a large number of pimples on itsinside face, and the above resin composition was injected around thecore by injection molding to form a cover with a thickness of 1.5 mm. Alarge number of dimples having a shape that is the inverted shape of thepimples were formed on the cover. A clear paint including atwo-component curing type polyurethane as a base material was applied tothis cover to obtain a golf ball of Example 1 with a diameter of 42.7 mmand a weight of about 45.4 g. The golf ball has a PGA compression ofabout 85. The golf ball has a dimple pattern shown in FIGS. 2 and 3. Theoccupation ratio of the golf ball is 92%. The total volume of thedimples of the golf ball is 690 mm³.

Example 2 and Comparative Examples 1 to 8

Golf balls of Example 2 and Comparative Examples 1 to 8 were obtained inthe same manner as Example 1, except the final mold was changed. Thespecifications of the dimples of these golf balls are shown in Tables 2and 3 below.

[Flight Distance Test]

Trajectory calculation was performed using aerodynamic characteristicvalues obtained through an ITR test. The conditions for the trajectorycalculation are as follows.

Ball initial speed: 57.4 m/s

Launch angle: 13.3°

Initial backspin rate: 2450 rpm

The average, in each segment, of the drag coefficients CD obtained bythe trajectory calculation is shown in Tables 2 and 3 below. Theaverage, in each segment, of the lift coefficients CL obtained by thetrajectory calculation is shown in Tables 2 and 3 below. In addition,the flight distance (carry) obtained by the trajectory calculation isshown in Tables 2 and 3 below. The flight distance is the distance fromthe launch point to the landing point.

TABLE 2 Results of Evaluation Comp. Comp. Comp. Comp. Comp. Example 1Example 2 Example 3 Example 4 Example 5 Pattern A A A B B Front FIG. 15FIG. 15 FIG. 15 FIG. 17 FIG. 17 view Plan FIG. 16 FIG. 16 FIG. 16 FIG.18 FIG. 18 view Total 532 552 572 536 556 volume (mm³) CD1 0.230 0.2260.228 0.227 0.223 CL1 0.188 0.179 0.177 0.188 0.178 CD2 0.266 0.2560.255 0.262 0.250 CL2 0.238 0.226 0.223 0.236 0.222 CD3 0.248 0.2590.273 0.233 0.257 CL3 0.178 0.211 0.236 0.168 0.216 CD4 0.221 0.2400.262 0.199 0.242 CL4 0.131 0.184 0.221 0.118 0.195 Carry 197.59 199.35199.08 199.26 200.79 (yard)

TABLE 3 Results of Evaluation Comp. Comp. Comp. Example 6 ExampleExample 1 Example 2 Example 8 Pattern B C C C C Front FIG. 17 FIG. 2FIG. 2 FIG. 2 FIG. 2 view Plan FIG. 18 FIG. 3 FIG. 3 FIG. 3 FIG. 3 viewTotal 576 670 690 710 730 volume (mm³) CD1 0.225 0.226 0.223 0.224 0.226CL1 0.177 0.187 0.177 0.175 0.173 CD2 0.252 0.265 0.245 0.244 0.243 CL20.221 0.237 0.215 0.212 0.209 CD3 0.271 0.244 0.265 0.270 0.273 CL30.236 0.182 0.230 0.239 0.245 CD4 0.259 0.231 0.256 0.266 0.276 CL40.222 0.163 0.213 0.234 0.245 Carry 200.22 198.71 200.91 200.90 200.50(yard)

As shown in Tables 2 and 3, the golf ball of each Example has excellentflight performance. From the results of evaluation, advantages of thepresent invention are clear.

The dimple pattern described above is applicable to a one-piece golfball, a multi-piece golf ball, and a thread-wound golf ball, in additionto a two-piece golf ball. The above descriptions are merely illustrativeexamples, and various modifications can be made without departing fromthe principles of the present invention.

What is claimed is:
 1. A golf ball having a large number of dimples on asurface thereof, wherein each dimple has a contour shape that isnon-circular, each dimple has a radius variation range Rh that is equalto or greater than 0.4 mm, if a trajectory is calculated underconditions that include a ball initial speed of 57.4 m/s, a launch angleof 13.3°, and an initial backspin rate of 2450 rpm by a program createdaccording to a manual provided by the USGA using a drag coefficient CDand a lift coefficient CL obtained through an ITR, and the trajectory isdivided into a first segment from a launch point to a midpoint betweenthe launch point and a top, a second segment from the midpoint betweenthe launch point and the top to the top, a third segment from the top toa midpoint between the top and a landing point, and a fourth segmentfrom the midpoint between the top and the landing point to the landingpoint, the first segment has an average CD1 of drag coefficients CD thatis equal to or less than 0.225, the first segment has an average CL1 oflift coefficients CL that is equal to or less than 0.180, the secondsegment has an average CD2 of drag coefficients CD that is equal to orless than 0.250, the second segment has an average CL2 of liftcoefficients CL that is equal to or less than 0.220, the third segmenthas an average CD3 of drag coefficients CD that is equal to or greaterthan 0.260, the third segment has an average CL3 of lift coefficients CLthat is equal to or greater than 0.220, the fourth segment has anaverage CD4 of drag coefficients CD that is equal to or greater than0.250, and the fourth segment has an average CL4 of lift coefficients CLthat is equal to or greater than 0.200.
 2. The golf ball according toclaim 1, wherein each dimple is obtained based on a contour of a Voronoiregion assumed on a surface of a phantom sphere of the golf ball.
 3. Thegolf ball according to claim 2, wherein a pattern of the dimples isobtained by a designing process comprising the steps of: (1) assuming alarge number of circles on the surface of the phantom sphere; (2)assuming a large number of generating points based on positions of thelarge number of circles; (3) assuming a large number of Voronoi regionson the surface of the phantom sphere by a Voronoi tessellation based onthe large number of generating points; and (4) assigning a dimple and aland to the surface of the phantom sphere based on contours of the largenumber of Voronoi regions.
 4. The golf ball according to claim 1,wherein each dimple satisfies the following mathematical formula:Rh/Rave≧0.25, wherein, in the mathematical formula, Rh represents aradius variation range, and Rave represents an average radius.
 5. Thegolf ball according to claim 1, wherein a difference between a radiusvariation range Rhmax of a dimple having a maximum radius variationrange Rh and a radius variation range Rhmin of a dimple having a minimumradius variation range Rh is equal to or greater than 0.1 mm.